The mean dynamic topography (MDT) can be computed as the difference between the mean sea level (MSL) and a gravimetric geoid. This requires that both data sets are spectrally consistent. In practice, it is quite common that the resolution of the geoid data is less than the resolution of the MSL data, hence, the latter need to be low-pass filtered before the MDT is computed. For this purpose conventional low-pass filters are inadequate, failing in coastal regions where they run into the undefined MSL signal on the conti- nents. In this paper, we consider the use of a bandlimited, spa- tially concentrated Slepian basis to obtain a low-resolution approximation of the MSL signal. We compute Slepian func- tions for the oceans and parts of the oceans and compare the performance of calculating the MDT via this approach with other methods, in particular the iterative spherical harmonic approach in combination with Gaussian low-pass filtering, and various modifications. Based on the numerical experi- ments, we conclude that none of these methods provide a low- resolution MSL approximation at the sub-decimetre level. In particular, we show that Slepian functions are not appropriate basis functions for this problem, and a Slepian representation of the low-resolution MSL signal suffers from broadband leakage. We also show that a meaningful definition of a low- resolution MSL over incomplete spherical domains involves orthogonal basis functions with additional properties that Slepian functions do not possess. A low-resolution MSL signal, spectrally consistent with a given geoid model, is obtained by a suitable truncation of the expansions of the MSL signal in terms of these orthogonal basis functions. We compute one of these sets of orthogonal basis functions using the Gram-Schmidt orthogonalization for spherical harmon- ics. For the oceans, we could construct an orthogonal basis only for resolutions equivalent to a spherical harmonic degree 36. The computation of a basis with a higher resolution fails due to inherent instabilities. Regularization reduces the insta- bilities but destroys the orthogonality and, therefore, pro- vides unrealistic low-resolution MSL approximations. More research is needed to solve the instability problem, per- haps by finding a different orthogonal basis that avoids it altogether.